Laura,
To expand on what Jon mentioned:
If you want any log comment to trigger a notification you just need to go to the Administration tab, go to
"Activity Notification" and find "Log Comment". Open it.
Under the "Notification Rule" tab there should be a default notification that will send, but "Auto Notification" is set to "No". Click the Rule to open it in a new window.
On the "Rules" details screen under the "Object Contacts" you can add values of who would get the notification.
This is the same screen where you'd define a "Condition", as Jon mentioned above to restrict it to certain situations.
Click the "Message Template" link, also on the same screen.
When the Message Template opens edit it and check "Auto Notification".
This will allow the notification to get sent out, but if you want to restrict it you'll need to make sure to get the Condition set up exactly as desired.